user
Below is an instruction that describes a task, paired with an input that provides further context. Write a response that appropriately completes the request.

### Instruction:
Compute the area of the triangle using Cartesian coordinates.

### Input:
x1 = 0,  y1 = 0,  x2 = 7,  y2 = 3,  x3 = 11,  y3 = 6

### Response:
assistant
The area of the triangle is 15.

Proof:

Let A (x1, y1), B (x2, y2) and C (x3, y3) be three points in the Cartesian plane. 

The area of triangle ABC is given by:

Area = 1/2 * |x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)|
  
= 1/2 * |0(3 – 6) + 7(6 – 0) + 11(0 – 3)|

= 1/2 * |0 – 21 + 42 + 0|

= 15